Critical Interfaces in Organic Solar Cells and Their Influence on the

Critical Interfaces in Organic Solar Cells and Their Influence on the Open-Circuit Voltage WILLIAM J. POTSCAVAGE, JR., ASHA SHARMA, AND BERNARD KIPPELEN* Center for Organic Photonics and Electronics (COPE), School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 RECEIVED ON MAY 1, 2009

CON SPECTUS

O

rganic photovoltaics, which convert sunlight into electricity with thin films of organic semiconductors, have been the subject of active research over the past 20 years. The global energy challenge has greatly increased interest in this technology in recent years. Low-temperature processing of organic small molecules from the vapor phase or of polymers from solution can confer organic semiconductors with a critical advantage over inorganic photovoltaic materials since the high-temperature processing requirements of the latter limit the range of substrates on which they can be deposited. Unfortunately, despite significant advances, the power conversion efficiency of organic solar cells remains low, with maximum values in the range of 6%. A better understanding of the physical processes that determine the efficiency of organic photovoltaic cells is crucial to enhancing their competitiveness with other thin-film technologies. Maximum values for the photocurrent can be estimated from the light-harvesting capability of the individual molecules or polymers in the device. However, a better understanding of the materials-level processes, particularly those in layerto-layer interfaces, that determine the open-circuit voltage (VOC) in organic solar cells is critical and remains the subject of active research. The conventional wisdom is to use organic semiconductors with smaller band gaps to harvest a larger portion of the solar spectrum. This method is not always an effective prescription for increasing efficiency: it ignores the fact that the value of VOC is generally decreased in devices employing materials with smaller band gaps, as is the case with inorganic semiconductors. In this Account, we discuss the influence of the different interfaces formed in organic multilayer photovoltaic devices on the value of VOC; we use pentacene-C60 solar cells as a model. In particular, we use top and bottom electrodes with different work function values, finding that VOC is nearly invariant. In contrast, studies on devices incorporating hole-transport layers with different ionization potentials confirm that the value of VOC depends largely on the relative energy levels of the donor and acceptor species that form the essential heterojunction. An analysis of the properties of solar cells using equivalent-circuit methods reveals that VOC is proportional to the logarithm of the ratio of the photocurrent density Jph divided by the reverse saturation current density J0. Hence, an understanding of the physical origin of J0 directly yields information on what limits VOC. We assign the physical origin of J0 to the thermal excitation of carriers from the donor to the acceptor materials that form the organic heterojunction. Finally, we show that the solution to achieving higher power conversion efficiency in organic solar cells will be to control simultaneously the energetics and the electronic coupling between the donor and acceptor materials, in both the ground and excited state.

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Published on the Web 08/26/2009 www.pubs.acs.org/acr 10.1021/ar900139v CCC: $71.50 © 2009 American Chemical Society

Influence of Interfaces on VOC in Organic Solar Cells Potscavage et al.

1. Introduction

Efficiency can be rewritten using these two parameters as

Organic solar cells have the potential to become ubiquitous

η)

power sources that are inexpensive, lightweight, and flexible,1-3 provided that their power conversion efficiency can be further increased. Compared with inorganic solar cells

|JMAX|VMAX |JSC|VOC × 100% ) FF × 100% IL IL

with the fill-factor FF defined by

where the active layers are generally chosen from a small

FF )

pool of materials, the list of compounds used to make organic solar cells is constantly expanding as previous molecules and polymers are modified to make new compounds with different properties. With so much freedom to modify organic molecules, an understanding of how material properties affect solar cell performance is needed to help guide the design of new compounds. While there is no physical model yet to describe all of the processes in organic solar cells, simple models relating material properties to performance are desirable

(2)

|JMAX|VMAX |JSC|VOC

(3)

Figure 1 depicts a typical J-V curve for a device based on a pentacene/C60 heterojunction9-11 in the dark and under illumination with JMAX, VMAX, JSC, and VOC all noted. Bathocuproine (BCP) is used as an interlayer layer between the C60 and the Al cathode. The physical processes limiting values for JSC and VOC in organic solar cells must be understood to design new materials for efficient devices because of their relationship to efficiency.

because they can help in the quest for solar cells with higher

2. Origin of the Short-Circuit Current

efficiencies. Power conversion efficiency is the most discussed parameter used to evaluate solar cell performance. While many people suggest that an efficiency of at least 10% is necessary for organic solar cells to establish a viable market, the highest efficiencies achieved in organic devices to date are around 5-6%.4-8 Efficiency is the percentage of input power from the light source that is converted to output power at the operating point where the device produces the maximum power and is written as

η)

PMAX |JMAX|VMAX × 100% ) × 100% PIN IL

The short-circuit current is directly related to the number of photons that are absorbed from the light source to form excitons, the conversion of excitons into electrons and holes, and the efficiency of charge transport to and charge collection at the electrodes. In organic solar cells, absorbed photons lead to bound electron-hole pairs, or excitons. To contribute to the photogenerated current, an exciton must first be dissociated into an electron and a hole. Efficient dissociation can occur at the essential heterojunction formed at the interface between a donor and acceptor material if the exciton binding energy

(1)

where PMAX is the maximum output power, PIN is the input power, JMAX and VMAX are the current density and voltage, respectively, at the point where PMAX is produced, and IL is the irradiance of the source. Two other key points of interest are at the boundaries in the current-density-voltage (J-V) characteristic where a device begins producing power. Short-circuit current density (JSC) is the current density when the voltage across a device is zero, and open-circuit voltage (VOC) is the voltage when the current density in the device is zero. Because power is the product of current and voltage and either current or voltage is zero at both of these points, there is no power production at either of these points. However, JSC and VOC are useful in that they represent the maximum current density and voltage that can be produced by the illumination of the device.

FIGURE 1. (a) Chemical structures of pentacene, C60, and BCP and (b) typical J-V curves for a pentacene/C60 device in the dark (dashed line) and in the light (solid line) with key performance parameters noted.

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FIGURE 2. Schematics of the basic structures for solar cells based on a planar heterojunction and on a bulk heterojunction.

is less than the energy lost in transferring the electron to the acceptor and the hole to the donor. This interface becomes a charge-injecting contact for electrons and holes on either side of the interface, and carriers travel to their respective electrodes under the gradient of the total electrochemical potential that acts as the driving force and generates the current in the device. Two main architectures exist for combining the donor and acceptor materials in organic solar cells, as shown in Figure 2: the planar heterojunction12 and the bulk heterojunction.13 Planar heterojunctions consist of organic layers sequentially deposited on top of one another and are generally vacuum deposited. With a bulk heterojunction, the donor and acceptor materials are blended together to make an active layer where donor and acceptor interfaces are dispersed throughout the bulk. Bulk heterojunctions benefit from a larger donor-acceptor interface area, potentially resulting in fewer excitons lost to recombination before dissociation. However, the morphology must provide continuous pathways through the donor and acceptor materials for holes and electrons to travel to the electrodes, and getting such a morphology that is thermodynamically stable can be difficult. In either case, the photocurrent depends on the absorption spectra of the active materials in the device and the spectrum of the light source. While the spectrum of incident sunlight depends on factors such as the location on the earth and cloud coverage, the AM1.5 G solar spectrum shown in Figure 3a is often used as a standard reference spectrum for comparing the efficiency of different solar cells. The dashed line in Figure 3a indicates the amount of current that could be generated if all of the photons up to each wavelength were absorbed and converted into current. The amount of current generated can clearly be increased by broadening the absorption spectra of the active materials in a solar cell with a maximum of ∼50 mA/cm2 available between 300 and 1350 nm. External quantum efficiency (EQE) defines the percentage of incident photons at a give wavelength that are converted into current. Figure 3b shows the EQE for a device based on a pentacene/C60 heterojunction.14 The JSC that is expected to 1760


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FIGURE 3. (a) Spectral photon flux density of the AM1.5 G solar spectrum (solid line) with the cumulative photon current density from zero up to each wavelength for all of the photons in the spectrum (dashed line) and for the EQE shown in panel b (shortdashed line). (b) Experimental EQE for a pentacene/C60 device (symbols) and fits to the model using an exciton diffusion length of 19 nm for C60 and varying between 20 and 80 nm for pentacene. The arrow indicates the direction of increasing exciton diffusion length for pentacene.

be generated in a device by a given light source can be calculated by multiplying the EQE with the incident spectrum and integrating. The short-dashed line in Figure 3a shows the cumulative photocurrent density for the pentacene/C60 device and the AM1.5 G spectrum. A JSC of 8.2 mA/cm2 is calculated for this device, and this value does not increase past ∼750 nm because of the lack of absorption in the cell after that wavelength. Because JSC can be calculated from the EQE, models that predict EQE are useful when designing new materials for solar cells. For planar-heterojunction cells, EQE can be modeled by calculating the optical field and exciton distribution in the device using the optical constants, layer thicknesses, and exciton diffusion lengths of the different layers.14-16 The distribution of excitons is calculated from a one-dimensional diffusion model with the optical field distribution determining the exciton generation rate and the boundary conditions that there are no excitons at the donor-acceptor interface because of efficient separation. Furthermore, a surface recom-

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bination velocity can be defined at the boundaries to describe the rate of recombination caused by the interfaces such as those formed with electrodes, but is often assumed in first approximation to be negligible. One additional parameter needed for the diffusion model is the exciton diffusion length, which is the average length an exciton travels before recombination. Finally, the rate of excitons arriving at the interface can be computed from the distribution and related to the current and EQE in the device.14 This model can then be used to estimate the exciton diffusion lengths in the materials by fitting the model to experimental EQE with the exciton diffusion lengths as fitting parameters. The solid lines in Figure 3b are EQE spectra calculated using the model with an exciton diffusion length in C60 of 19 nm and in pentacene of 20-80 nm.14 An exciton diffusion length of ∼70 nm in pentacene yields EQE spectra that are very close to the experimental data. From the optical data and by assuming values for the exciton diffusion lengths, the EQE and JSC in planar-heterojunction devices can be predicted for new materials. While this model cannot strictly be applied to bulk-heterojunction devices because of their more complex morphology, the mechanisms leading to current generation in multilayer organic solar cells are fairly well understood. The absorption spectra and exciton diffusion lengths of the organic layers play a key role in determining the JSC. Since efficiency is proportional to JSC, developing materials with low band gaps and broad absorption spectra might seem like the best route for increasing efficiency. However, efficiency is also proportional to VOC, and decreasing the band gap often comes at the expense of decreasing VOC. For this reason, the origin of VOC in organic solar cells must also be studied and better understood.

3. Origin of the Open-Circuit Voltage The processes governing VOC in organic solar cells are less obvious from a conceptual standpoint than those related to JSC and are still the subject of much debate. By definition, VOC is the voltage across a cell under illumination when there is no current flowing through the device. While there is still a photocurrent being generated by the light, the photocurrent is being offset by other currents in the device, netting zero current flow out of the contacts. Originally, VOC was thought to be determined by the difference in the work function of the two electrodes used to make a device.17 More recent studies have shown a correlation between VOC and the difference between the highest occu-

FIGURE 4. (a) Equivalent circuit model for solar cells and (b) fits for a pentacene/C60 device in the dark and light using the equivalent circuit model.

pied molecular orbital (HOMO), or ionization potential, of the donor and the lowest unoccupied molecular orbital (LUMO), or electron affinity, of the acceptor used in both planar-heterojunction18-20 and bulk-heterojunction21-25 solar cells. These observations suggest that decreasing the band gap of the organic layers to increase the absorption will also decrease VOC because of a reduced HOMO-LUMO energy difference. More insight into VOC can be gained by studying how material properties affect the J-V characteristics of a device, which ultimately determine the operation of any device. 3.1. Equivalent Circuit Model. The equivalent circuit model that was originally developed to simulate and understand the J-V characteristics of inorganic solar cells can also be applied to organic solar cells.26,27 The model uses several basic circuit elements that each account for different processes in a solar cell, and J-V curves can be calculated from the circuit using basic circuit theory. Figure 4a shows a schematic of the equivalent circuit, which consists of a parallel-connected current source, diode, and parallel resistance connected in series with an additional series resistance. The current source represents the photocurrent Jph generated in the device when under illumination. This term will depend on the spectrum and intensity of the incident light; thus, Jph is zero for a device in the dark. The diode accounts for the rectifying behavior of the donor-acceptor heterojunction and is characterized by the reverse saturation current density J0 and the ideality factor n. Because diodes follow an exponential curve, the reverse saturation current density is the

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current density of an ideal diode when biased with a nega-

VOC ) n

tive voltage. The ideality factor is related to the slope of the exponential curve, with an ideal diode having an n of unity. Ideality factors greater than unity yield exponential curves that

≈n

JSC kT ln 1 + e J0

≈n

JSC kT ln e J0

increase more slowly and may be caused by factors such as recombination currents. The parallel resistance RPA allows for leakage currents that are not attributed to the diode from sources such as recombination and pinholes. Ideally, RPA should be high to minimize losses from current circumventing the load. Finally, the series resistance RSA accounts for the finite resistance of the organic layers and electrodes along with the contact resistance between each of the interfaces. The series resistance prevents the exponential diode from increasing to infinitely large currents and should be small to minimize electrical power losses caused by the resistance limiting the current in the device. From the equivalent circuit model, the equation for the J-V characteristics of a solar cell can be derived as

J)

[{ (

) } (

V - JRSA 1 V J0 exp - 1 - Jph 1 + RS ⁄ RP nkT ⁄ e RPA

)]

(4)

where k is the Boltzmann constant, T is the temperature, e is the elementary charge, and A is the area of the device. This equation can be fitted to experimental data using RS, RP, J0, and n as the fitting parameters. Comparison of these parameters for devices with different materials and geometries can then yield information on how the changes affect different aspects of the device. Figure 4b shows fits to the model in the light and dark for a cell with the geometry indium-tin oxide (ITO)/pentacene (50 nm)/C60 (45 nm)/BCP (8 nm)/Al. Looking at the region where the device is producing power from 0 to 0.4 V, the equivalent circuit model closely follows the behavior of the device. Furthermore, the semilogarithmic plots indicate that the model can also fit more than just the power-producing region of the J-V curves with good agreement all the way out to (1 V. Details of the fitting procedure can be found elsewhere.14 Because of the ability of the model to reproduce the behavior of an actual device, the equivalent circuit can be used to better understand what determines VOC. Open-circuit voltage can be calculated from eq 4 by setting the current to zero and solving for the voltage, yielding 1762


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{ ( { } { }

Jph VOC kT 1ln 1 + e J0 JphRpA

)}

(5)

with the approximations coming from the assumptions that RPA is large and RSA is small. For most good devices, JSC values tend to be within one order of magnitude. Therefore, the parameters with the most impact on the VOC are expected to be J0 and n. To investigate what properties of a device affect the J0 and n and determine VOC, three modifications to interfaces in ITO/ pentacene/C60/BCP/Al devices have been carried out in this study. First, the work function of the ITO anode was varied by using different surface modifications. If the work function of the electrodes has the greatest impact on VOC, then changes in both the VOC and circuit parameters can be anticipated. Similarly, the work function of the cathode was varied by using the low work function metal Ca (2.9 eV) in place of Al (4.2 eV). Figure 5 depicts the energy level diagram for a pentacene/ C60 solar cell and the changes in work function that have been explored by modifying the anode and cathode. Finally, the donor layer was replaced with compounds having different HOMO values, and their effect was analyzed with the equivalent circuit model. All of the device data and efficiencies presented here were measured under illumination of a filtered broadband light source and are not exact values for the AM1.5 G spectrum, but the general trends that are the focus of this Account should hold for AM1.5 G. 3.2. Anode Modification. One way to modify the work function of the anode is through surface modification of the ITO. We have recently reported on the changes in the work function of ITO accomplished by either the incorporation of organic surface modifiers or air plasma treatment.28-30 The organic modifiers composed of a phosphonic acid moiety, which attaches to the ITO surface, covalently bonded to various dipolar functional groups. Kelvin probe measurements show that the ITO work function can be varied between 4.5 eV for untreated ITO and 5.4 eV for ITO treated with air plasma. Use of pentafluorobenzyl phosphonic acid (F5BPA) on the surface of the ITO resulted in a work function value of 4.9 eV. Devices were fabricated by vacuum thermal evaporation on top of the modified ITO with the geometry ITO/surface modifier/pentacene (50 nm)/C60 (45 nm)/BCP (8 nm)/Al (200 nm). Details about the surface modification and device fabrication

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ure 6b shows the experimental data with the fits using the parameters listed in Table 1. With very little difference between each of the parameters, changing the work function of the ITO with surface modification does not appear to have any significant impact on the device that can be associated with a particular parameter or process. Furthermore, modeling of diodes based on single layers of pentacene sandwiched between modified ITO and Al electrodes suggests that the bar-

FIGURE 5. Energy level diagram for a pentacene/C60 device.

rier for injection into the pentacene does not significantly change with the ITO work function, which may be the result of Fermi level pinning.30 These results show that the work function of the anode does not necessarily have a strong influence on VOC for organic solar cells. However, the use of different anodes could still significantly alter device performance for other reasons, such as if the morphology of the active layer is modified or if the anode is too resistive. 3.3. Use of Different Cathodes. Next, metals with different work functions were used as the cathode to continue to investigate how the work function difference between the two electrodes affects VOC in organic solar cells. Pentacene/C60 devices were made using the same procedures as in ref 30 without any surface modification to the ITO, but either Al or Ca was deposited as the cathode. With a work function of 2.9 eV, Ca has a work function that is 1.3 eV lower than that of Al and should lead to a large increase in VOC if organic solar cells follow the operation of metal-insulator-metal devices. FIGURE 6. (a) Experimental data for pentacene/C60 devices on ITO with different surface modifications: unmodified (0), F5BPA (O), and air plasma (4). Solid lines are fits to the circuit model in the dark. (b) The same data on a semilogarithmic plot over a wider range of voltages along with the structure of F5BPA.

can be found in ref 30. Figure 6a shows the J-V characteristics for the devices in the dark and under illumination. Table 1 summarizes the performance parameters for each geometry averaged over three devices. Even with a large change in work function of the ITO, no significant difference in VOC, JSC, or FF is observed. To verify that changing the work function of the ITO has no effect on the parameters of the equivalent circuit model, experimental data in the dark were fitted to the model. Fig-

Figure 7 shows the experimental J-V curves for the devices in the dark and under illumination, and the performance parameters averaged over three samples for each cathode are summarized in Table 2. The devices with Ca as the cathode yield VOC values only 5 mV larger than the Al cathode devices despite the difference of 1.3 eV in work function. Only JSC differs significantly for the Ca devices and is ∼33% smaller than that of the Al devices. The decrease in JSC can be attributed to the lower reflectance of Ca compared with that of Al, which gives less light a second pass through the device and a second chance at absorption.31 The lower values in VOC and JSC compared with the surface-modified devices are within the range expected for batch-to-batch variations.

TABLE 1. Performance Parameters for Pentacene/C60 Solar Cells on ITO with Different Surface Modifications and Fitting Parameters for the Equivalent Circuit Model surface modifier

VOC (mV)

|JSC| (mA/cm2)

FF

η (%)

J0 (µA/cm2)

n

RSA (Ω cm2)

RPA (kΩ cm2)

unmodified F5BPA air plasma

405 ( 2 399 ( 2 402 ( 1

13 ( 1 13 ( 0.2 12 ( 0.4

0.55 ( 0.01 0.55 ( 0.01 0.56 ( 0.01

3.8 ( 0.1 3.7 ( 0.1 3.6 ( 0.1

0.225 0.295 0.196

1.53 1.56 1.52

0.648 0.708 0.600

298 375 247

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FIGURE 7. Experimental data for pentacene/C60 devices with different cathodes: Al (0) and Ca (O). The solid line is a model fit for the Al device and the dashed line for the Ca device. The inset shows the same data on a semilogarithmic scale.

Here again, the equivalent circuit model can be used to more closely evaluate whether the change in cathode had any significant impact on the device that is not obvious by just observing the J-V graphs. Included in Figure 7 are lines calculated from fits to the experimental data in the dark using the parameters in Table 2. Though there is a small difference in J0 most likely related to batch-to-batch variations, the difference is not large enough to significantly affect VOC because what matters in eq 5 is ln(JSC/J0), so much bigger changes in J0 must be made to impact VOC 3.4. Effect of Donor on Open-Circuit Voltage. Finally, the pentacene layer was replaced with the donors copper phthalocyanine (CuPc) and titanyl phthalocyanine (TiOPc). These donors were chosen because of their difference in HOMO levels, with pentacene having the lowest and TiOPc the highest.32-34 Figure 8a shows the chemical structures of the phthalocyanines along with the general device architecture used for all of the devices. Details on the device fabrication and testing can be found in ref 35. Figure 8b shows the J-V curves for the solar cells with the three different donors in the dark and under illumination. Table 3 lists the performance parameters for each device. Open-circuit voltage in these devices increases with the HOMO of the donor. Fits were made by applying the circuit model and are shown in Figure 8b for the parameters in Table 3. The fitting data confirms that J0 decreases as VOC increases, with a decrease of almost an order of magnitude in J0 from penta-

FIGURE 8. (a) Chemical structures of CuPc and TiOPc, and the test structure used for the donor/C60 cells. (b) Dark J-V characteristics for donor/C60 cells where the donor is either pentacene (O), CuPc (0), or TiOPc (4). The straight lines are fits using the parameters in Table 3. Inset shows J-V curves under illumination for the same devices.

cene to CuPc to TiOPc. While the value of J0 for this pentacene device is higher than those for previously presented devices, the increase is accompanied by the expected decrease in VOC and may be caused by purity differences in this batch. Clearly, the origin of J0 must be better understood because of its impact on VOC. Analysis of J0 in the dark for the pentacene device revealed that J0 as a function of temperature, shown in Figure 9, can be fitted with the thermally activated injection expression

( )

J0 ) J00 exp

(

-φB -∆EHL ) J00 exp kT n'kT

)

(6)

with an activation energy φB ) 0.55 eV and a prefactor J00 ) 3090 A/cm2 over the measured temperature range from 275 to 336 K. The activation energy φB can be rewritten as ∆EHL/ n′, where ∆EHL is the difference between the HOMO of the donor and the LUMO of the acceptor before junction formation and n′ is a factor that accounts for effects such as the formation of charge-transfer states36 and vacuum level misalignments at the heterojunction caused by energy level

TABLE 2. Performance Parameters for Pentacene/C60 Solar Cells with Different Cathodes and Fitting Parameters for the Equivalent Circuit Model cathode

VOC (mV)

|JSC| (mA/cm2)

FF

η (%)

J0 (µA/cm2)

n

RSA (Ω cm2)

RPA (kΩ cm2)

Ca Al

371 ( 2 367 ( 2

8.1 ( 0.1 12.1 ( 0.4

0.56 ( 0.01 0.54 ( 0.01

2.2 ( 0.1 3.1 ( 0.1

0.615 0.414

1.62 1.46

1.09 1.53

48.4 60.1

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kt )

(

(∆G0 + λ)2 1 exp 4πλkT 4λkT

2π 2 |V | p if

)

(8)

where λ is the reorganization energy induced by the electron transfer, ∆G0 is the variation of the Gibbs free energy during the reaction, and Vif is the electronic coupling matrix element.39 The steady-state reverse saturation current density can also be written as FIGURE 9. J0 at different temperatures for a pentacene/C60 device (0) and fit using eq 6 with J00 ) 3090 A/cm2 and φB ) 0.55 eV (solid line).

J0 ) ektNCT

(9)

where e is the elementary charge and NCT is the surface den-

bending and interface dipoles that reduce the activation

sity of interacting donor and acceptor pairs that can be ther-

energy from ∆EHL.

mally excited with a rate kt given by eq 8. By combining eqs

A final equation for VOC can be obtained using eqs 5 and

6, 8, and 9, the prefactor J00 can also be expressed as

6 as

{ }

{ }

J00 J00 n eVOC ) nφB - nkT ln ) ∆EHL - nkT ln JSC n' JSC

J00 ) eNCT (7)

1 4πλkT

2π 2 |V | p if

(10)

and the thermal activation barrier φB in eq 6 can be correlated with (∆G0 + λ)2/(4λ) in the argument of the exponen-

Values of J0 and VOC calculated for each of the devices with

tial term in the Marcus expression in eq 8. This analysis shows

different φB are listed in Table 4 and show good agreement

that the reverse saturation current density is strongly influ-

with the experimental values. We note that φB is lower than

enced by the molecular energy levels of the donor and accep-

∆EHL. This was expected because of various physical processes

tor molecules that form the organic heterojunction. However,

that can occur at the interface when the donor and acceptor

eq 10 illustrates that the electronic coupling and reorganiza-

materials are brought into contact. Measured values of the gap

tion energy are equally important in influencing the reverse

at CuPc/C60 interfaces of ∼0.7 eV agree with the value of 0.6

saturation current. Hence, as donor and acceptor materials are

eV calculated here.20,37,38

designed for future high-efficiency organic solar cells, great

The first term in eq 7 shows the importance of ∆EHL in

consideration must be given to their molecular shape, geom-

influencing VOC, and the second term suggests that VOC will

etry, charge densities, relaxation due to vibrational modes,

decrease as J00 increases. To understand the correlation

and packing. The energetics and electronic coupling between

between molecular structure and the open-circuit voltage in

donor/acceptor molecules and polymers will simultaneously

organic solar cells, we turn now to a brief discussion of the

impact the short-circuit current and the open-circuit voltage. To

physical origin of the reverse saturation current. We had pre-

maximize exciton dissociation, large energy level offsets and

viously assigned its origin to the thermal excitation of carri-

a strong electronic coupling are desirable for charge transfer

ers at the donor/acceptor heterojunction through a reaction of

reactions of the type D* + A f D+ + A- or D + A* f D+ +

+

-

the type D + Af D + A in which an electron gets trans-

A- that involve molecules or polymers in the excited state. To

ferred from the HOMO of a donor molecule to the LUMO of

achieve large open-circuit voltages, large values for ∆EHL and

an acceptor molecule.35 The rate for such a reaction can be

a weak electronic coupling between the donor and acceptor

described at the molecular level by a semiclassical Marcus the-

materials are required for charge transfer reactions of the type

ory expression,

D + A f D+ + A-.

TABLE 3. Performance Parameters for Donor/C60 Solar Cells with Different Donors and Fitting Parameters for the Equivalent Circuit Model donor

VOC (mV)

|JSC| (mA/cm2)

FF

η (%)

J0 (µA/cm2)

n

RSA (Ω cm2)

RPA (kΩ cm2)

pentacene CuPc TiOPc

0.35 0.47 0.60

11.0 6.45 3.99

0.53 0.62 0.51

2.1 1.9 1.2

1.37 0.33 0.023

1.68 2.00 2.02

0.480 1.98 0.413

110 43.9 1970

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Since 2003, he has been Professor of Electrical and Computer Engineering at the Georgia Institute of Technology, Atlanta, GA. He is a Fellow of the Optical Society of America, a Fellow of SPIE, and a Senior Member of IEEE.

TABLE 4. Values Calculated for Each Donor/C60 Cell Using Eq 7 with J00 ) 3090 A/cm2, n from Table 3, and T ) 300 K for the calculation of J0Th in the dark and 323 K for VOCTh under illumination donor

φB (eV)

J0Th (µA/cm2)

VOCTh (V)

pentacene CuPc TiOPc

0.55 0.60 0.67

1.55 0.26 0.02

0.34 0.47 0.59

FOOTNOTES * To whom correspondence should be addressed. E-mail address: kippelen@ ece.gatech.edu.

4. Conclusions Efficiency of organic solar cells is dependent on both the shortcircuit current and the open-circuit voltage of a device. While designing molecules with small band-gaps may be beneficial to absorbing more of the solar spectrum and increasing the short-circuit current, reduced band-gaps may also reduce the open-circuit voltage. We have shown through the use of an equivalent circuit model that the open-circuit voltage is related to the reverse saturation current. In the future, more must be done to understand how material properties affect the reverse saturation current and to create combinations of donor and acceptor molecules that can reduce the reverse saturation current. This material is based upon work supported in part by Solvay S.A., the STC Program of the National Science Foundation under Agreement Number DMR-0120967, the Office of Naval Research, and the Georgia Research Alliance. The authors thank the Marder group for synthesizing the surface modifier used to modify the work function of ITO and Professor N. R. Armstrong and M. Brumbach for providing the TiOPc device data. BIOGRAPHICAL INFORMATION William J. Potscavage, Jr. was born in Houston, TX, in 1982. He earned his B.S. (2003) and M.S. (2005) from the Georgia Institute of Technology and is currently pursuing his Ph.D. there. His interests include developing solar cells based on new polymers and small molecules and investigating the physics of device operation. Asha Sharma received her Ph.D. from IIT, Kanpur, India, in 2006. Following that, she was a postdoctoral fellow at the Georgia Institute of Technology, Atlanta, at the Center for Organic Photonics and Electronics in the School of ECE until 2008. She is currently a postdoctoral researcher at the University of Utah, Salt Lake City, in the department of Electrical and Computer Engineering where she is working on wireless integrated neural interfaces for biomedical devices. B. Kippelen received his Ph.D. in solid-state physics in 1990 from the University Louis Pasteur, Strasbourg, France. He was Charge´ de Recherches at the CNRS. In 1994, he joined the Optical Sciences Center at The University of Arizona where he became an Assistant Professor in 1998 and an Associate Professor in 2001. 1766


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